There had been attempts at body armor for awhile by that time. I do know that the Soviets issued steel armor to combat engineers and some of there assault units Dearing WW2. And the NATO forces started issuing armored vest to flight crews daring the same era.
The first ground combat armor started to be issued to USMC units for testing in 49. And was Also tested by the Army who adopted the armor in 51. And that's as my sleep deprived mind can remember at the moment.
http://en.wikipedia.org/wiki/M-1951_field_jacketDuring the Korean War several new vests were produced for the United States military, including the M-1951, which made use of fibre-reinforced plastic or aluminium segments woven into a nylon vest. These vests represented "a vast improvement on weight, but the armor failed to stop bullets and fragments very successfully," although officially they were claimed to be able to stop 7.62×25mm Tokarev pistol rounds at the muzzle. Developed by Natick Laboratories and introduced in 1967, T65-2 plate carriers were the first vests designed to hold hard ceramic plates, making them capable of stopping 7 mm rifle rounds.
from Wiki.
The Soviet Armed Forces used several types of body armor, including the SN-42 ("Stalnoi Nagrudnik" is Russian for "steel breastplate", and the number denotes the design year). All were tested, but only the SN-42 was put in production. It consisted of two pressed steel plates that protected the front torso and groin. The plates were 2 mm thick and weighed 3.5 kg (7.7 lb). This armor was supplied to SHISBr (assault engineers) and to Tankodesantniki (infantry that rode on tanks) of some tank brigades. The SN armor protected wearers from 9 mm bullets fired by an MP 40 at around 100 meters, which made it useful in urban battles such as the Battle of Stalingrad. However, the SN's weight made it impractical for infantry in the open.